Extrapolated ILDF stage requirements
Using the permeate removal data for the initial pass of the five
starting ethanol concentrations examined, a continuous ILDF (Figure 1C)
was modelled and the number of passes/stages for the target ethanol
removal calculated. Figure 4A shows the permeate removed for each of the
measured initial ethanol concentration passes with an extrapolated
curve/function. This function was used to model each independent
pass/stage of a continuous ILDF process until the target ethanol removal
was achieved (Figure 4B). Each pass/stage was modelled using the
following equations:
\(c_{p+1}=\frac{c_{p}R-c_{p}f\left(c_{p}\right)}{R}\) (Equation
4)\(f\left(c_{p}\right)=-5.696\ln\left(c_{p}\right)-3.8359\)(Equation 5)
where \(c_{p}\)= ethanol concentration at the beginning of a pass,\(c_{p+1}\)= ethanol concentration at the end of a pass, \(R\)= mass
of the retentate, and \(f(c_{p})\) = the extrapolated ethanol
concentration dependent permeate removal function. Using Equations 4 and
5, starting ethanol concentrations were selected and the ethanol
concentrations calculated after each subsequent pass/stage. The
calculation continued until the target ethanol removal was achieved and
the number of passes/stages determined.
The number of passes needed when starting at different concentrations
was calculated and are shown in Figure 4B. Figure 4C compares the
calculated pass/stage data to the pass/stage data determined with the
Figure 1D set up. The modelled continuous ILDF passes required are
significantly less than the Figure 1D set up, but the difference becomes
smaller with lower initial ethanol concentrations. This shows that the
impact of carrying through the Figure 1D initial ethanol concentration
limitation on permeability was mitigated by calculating the passes
independently. Note that the continuous ILDF ethanol reduction curve
does not follow the diafiltration equation, while the Figure 1D set up
did. This is most likely due to the Figure 1D reuse of the same hollow
fibers for each run, which caused the permeability limitations similar
to a CVDF batch process. The extrapolated ILDF model’s use of new hollow
fibers for each pass/stage leveled out the rejection coefficient effect
into a linear reduction as the permeability of each pass/stage was set
independently. Overall, this showed that a continuous ILDF process would
minimize any impact of the ethanol rejection coefficient or permeability
reduction as compared to the batch CVDF process.